Semiconductor device

ABSTRACT

According to one embodiment, a semiconductor device includes N fins made of a semiconductor material aligned in parallel with each other; a first gate electrode formed on both side surfaces of each of the N fins to cross the fins; and a second gate electrode formed in parallel with the first gate electrode on both side surfaces of the N fins to cross the fins, and having a larger gate length than a gate length of the first gate electrode, wherein number of fins formed with contacts of source/drain layers of first field-effect transistors having the first gate electrode is larger than number of fins formed with contacts of source/drain layers of second field-effect transistors having the second gate electrode.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a division of and claims the benefit of priorityunder 35 U.S.C. §120 from U.S. Ser. No. 12/494,885 filed Jun. 30, 2009,and claims the benefit of priority under 35 U.S.C. §119 from JapanesePatent Application No. 2008-199453 filed Aug. 1, 2008, the entirecontents of each of which are incorporated herein by reference.

BACKGROUND

In semiconductor integrated circuit devices, high performance and highlogic gate density integration of field-effect transistors are achievedby miniaturization of a gate length following the scaling rule anddecreasing a thickness of a gate dielectric film. However, if a gatelength of a field-effect transistor becomes equal to or smaller than 30nanometers, the influence of a short-channel effect should be large, anda cutoff characteristic should be degraded. Therefore, to obtain afavorable cutoff characteristic, there has been proposed a double-gatetransistor having fins formed on a silicon-on-insulator (SOI) substrateor on a bulk substrate, having a gate electrode manufactured to crossthe fins, and having channels formed at both sides of each fin.

According to such a double-gate transistor, the variation of a thresholdvoltage is small, the output resistance can be large. If double gatetransistors can be installed for the application of a base-band (lowfrequency) analog devices together with a digital devices, itsfabrication cost can be reduced because they are fabriacted by almostthe same process on the same wafer.

For example, Japanese Patent Application Laid-open No. 2006-269975discloses a method of reducing a parasitic resistance of fin portions ofa fin field-effect transistor (FinFET) and suppressing the variation ofthe resistance between a source and a channel and between a drain and achannel of the FinFET, by crystal epi-growth of a semiconductor layerconnecting between the fin portions, on an upper surface and sidesurfaces of the fin portions positioned at both sides of a gateelectrode.

However, the double-gate transistor has a very small width of fins, hasa large parasitic resistance, and has variation of the fin width.Therefore, if a base-band analog circuit is formed with a double-gatetransistor with larger parasitic resistance by using a similar designmethod for a bulk transistor formed on a bulk substrate, sufficient gaincannot be achieved or the characteristic variation of the analog circuitshould be degraded.

SUMMARY

A semiconductor device according to an embodiment comprises: N (N is aninteger equal to or larger than 2) fins made of a semiconductor materialaligned in parallel with each other; a first gate electrode formed onboth side surfaces of each of the N fins to cross the fins; and a secondgate electrode formed in parallel with the first gate electrode on bothside surfaces of the N fins to cross the fins, and having a larger gatelength than a gate length of the first gate electrode, wherein number offins formed with contacts of source/drain layers of first field-effecttransistors having the first gate electrode is larger than number offins formed with contacts of source/drain layers of second field-effecttransistors having the second gate electrode.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plan view of a layout configuration of a semiconductordevice according to a first embodiment;

FIG. 2 is a perspective view of a schematic configuration of a portion Bin FIG. 1;

FIG. 3 depicts an equivalent circuit of the semiconductor device shownin FIG. 1;

FIG. 4 is a plan view of a layout configuration of a semiconductordevice according to a second embodiment;

FIG. 5 depicts an equivalent circuit of the semiconductor device shownin FIG. 4;

FIG. 6A is a plan view of a method of manufacturing a fin structureaccording to a third embodiment;

FIG. 6B is a cross-sectional view of FIG. 6A cut along a line A1-A1′;

FIG. 7A is a plan view of the method of manufacturing a fin structureaccording to the third embodiment;

FIG. 7B is a cross-sectional view of FIG. 7A cut along a line A2-A2′;

FIG. 8A is a plan view of the method of manufacturing a fin structureaccording to the third embodiment;

FIG. 8B is a cross-sectional view of FIG. 8A cut along a line A3-A3′;

FIG. 9A is a plan view of the method of manufacturing a fin structureaccording to the third embodiment; and

FIG. 9B is a cross-sectional view of FIG. 9A cut along a line A4-A4′.

DETAILED DESCRIPTION OF THE INVENTION

Exemplary embodiments of a semiconductor device according to the presentinvention will be explained below in detail with reference to theaccompanying drawings. The present invention is not limited to theembodiments.

FIG. 1 is a plan view of a layout configuration of a semiconductordevice according to a first embodiment.

In FIG. 1, plural fins f11 to f19 and f21 to f29 are aligned in parallelwith each other. Preferably, the width of each of the fins f11 to f19and f21 to f29 is equal to each other, and the interval between fins ofthe fins f11 to f19 and f21 to f29 is equal to each other. Preferably,the total number of the fins f11 to f19 and the total number of the finsf21 to f29 are even numbers. A semiconductor material can be used forthe material of the fins f11 to f19 and f21 to f29. For examples, thematerial can be selected from Si, Ge, SiGe, SiC, SiSn, PbS, GaAs, InP,GaP, GaN, ZnSe, and GaInAsP.

For the fins f13 to f18, gate electrodes G11 are formed on both sidesurfaces of the fins f13 to f18 to cross the fins f13 to f18. For thefins f23 to f28, gate electrodes G12 are formed on both side surfaces ofthe fins f23 to f28 to cross the fins f23 to f28.

For the gate electrodes G11 and G12, gate electrodes G13 and G14 arealigned in parallel at a predetermined interval, respectively. For thefins f13 to f18, the gate electrodes G13 are formed on both sidesurfaces of the fins f13 to f18 to cross the fins f13 to f18. For thefins f23 to f28, the gate electrodes G14 are formed on both sidesurfaces of the fins f23 to f28 to cross the fins f23 to f28.

Further, for the gate electrodes G13 and G14, gate electrodes G15 arealigned at a predetermined interval. For the fins f13 to f18 and f23 tof28, the gate electrodes G15 are formed on both side surfaces of thefins f13 to f18 and f23 to f28 to cross the fins f13 to f18 and f23 tof28.

Preferably, the gate electrodes G11, G12, and G15 can have a larger gatelength than that of the gate electrodes G13 and G14. Preferably, a drainresistance in a saturation region of transistors having the gateelectrodes G11, G12, and G15 is set to be assumed that it issubstantially infinite (dI_(d)/dV_(d)=1/R_(d) to 0). Preferably, a gatelength of the gate electrodes G13 and G14 is set as small as possible toincrease mutual conductance and to increase gain, and can be set equalto or smaller than 30 nanometers, for example.

Source/drain layers are formed in the fins f13 to f18 and f23 to f28 atboth sides of the gate electrodes G11 to G15, respectively. Thesource/drain layers formed in the fins f13 to f18 between the gateelectrode G11 and the gate electrode G13 are shared by the gateelectrodes G11 and G13. The source/drain layers formed in the fins f23to f28 between the gate electrode G12 and the gate electrode G14 areshared by the gate electrodes G12 and G14. The source/drain layersformed in the fins f13 to f18 between the gate electrode G13 and thegate electrode G15 are shared by the gate electrodes G13 and G15. Thesource/drain layers formed in the fins f23 to f28 between the gateelectrode G14 and the gate electrode G15 are shared by the gateelectrodes G14 and G15.

The fins f13 and f15 at a drain side at the side of the gate electrodesG11 are connected to a wiring H11 via contacts C11, respectively. Thefins f23 and f25 at a drain side at the side of the gate electrodes G12are connected to the wiring H11 via contacts C12, respectively. The finsf13 to f18 at a source side at the side of the gate electrodes G11 areconnected to a wiring H12 via contacts C13, respectively. The fins f23to f28 at a source side at the side of the gate electrodes G12 areconnected to a wiring H13 via contacts C14, respectively.

The fins f13 to f18 and f23 to f28 at a drain side at the side of thegate electrodes G15 are connected to a wiring H14 via contacts C15 andC16, respectively. The fins f14 to f16 and f24 to f26 at a source sideat the side of the gate electrodes G15 are connected to a wiring H15 viacontacts C17 and C18, respectively. Metals such as Al and Cu can be usedfor the material of the wirings H11 to H15.

Preferably, the contacts C11 to C15 are symmetrically placed,respectively. Preferably, the gate electrodes G11 and G12 are alignedsymmetrically with each other. Preferably, the gate electrodes G13 andG14 are aligned symmetrically with each other. Preferably, the wiringsH12 and H13 are aligned symmetrically with each other. Embedded wiringsformed on the fins f13 to f18 and f23 to f28 can be used for thecontacts C11 to C15.

Out of the fins f11 to f19 and f21 to f29, the fins (f11 & f12) and (f21& f22) can be used as dummy fins; They can not be used as a part offield-effect transistors.

FIG. 2 is a perspective view of a schematic configuration of a portion Bin FIG. 1.

In FIG. 2, an isolation layer 12 is formed on a semiconductor substrate11, and the fins f26 to f28 are aligned in parallel on the isolationlayer 12. For the fins f26 to f28, the gate electrodes G14 are formed onboth side surfaces of the fins f26 to f28 via gate dielectric films 13 ato 13 c, respectively. Upper insulation films 14 a to 14 c are formedbetween upper surfaces of the fins f26 to f28 and the gate electrodesG14.

Because of no intentional doping into the fins f26 to f28, channelsformed in the fins f26 to f28 can be fully depleted and can operate asan intrinsic channel device. To adjust a threshold voltage offield-effect transistors formed in the fins f26 to f28, metal compoundssuch as titanium nitride, tantalum carbon, a lanthanum material, analuminum material, and a magnesium material can be used as a single unitor in combination, for the material of the gate electrodes G14.

FIG. 3 depicts an equivalent circuit of the semiconductor device shownin FIG. 1. The equivalent circuit is used for a common-mode feedback(CMFB) circuit or the like.

In FIG. 3, a constant current source 21 is connected to a drain of afield-effect transistor 25 via a resistor 23, and a constant currentsource 22 is connected to a drain of a field-effect transistor 26 via aresistor 24. A constant current source 27 is connected in common tosources of the field-effect transistors 25 and 26.

The constant current source 21 can be configured by the gate electrodesG11 and the fins f13 to f18 shown in FIG. 1. The constant current source22 can be configured by the gate electrodes G12 and the fins f23 to f28shown in FIG. 1. The field-effect transistor 25 can be configured by thegate electrodes G13 and the fins f13 to f18 shown in FIG. 1. Thefield-effect transistor 26 can be configured by the gate electrodes G14and the fins f23 to f28 shown in FIG. 1. The constant current source 27can be configured by the gate electrodes G15 and the fins f13 to f19 andf23 to f29 shown in FIG. 1. The resistor 23 can be related to parasiticresistances of the fins f13 to f18 between the gate electrode G11 andthe gate electrode G13. The resistor 24 can be related to parasiticresistances of the fins f23 to f28 between the gate electrode G12 andthe gate electrode G14.

The wiring H11 shown in FIG. 1 is connected to a power source potential(voltage) V_(dd), and the wiring H15 is connected to a ground potential(voltage) V_(ss). If input voltages V_(in1) and V_(in2) are applied tothe gate electrodes G13 and G14, respectively, output voltages V_(out1)and V_(out2) are output from the wirings H12 and H13, respectively,thereby causing the field-effect transistors operate as differentialamplifiers.

Even If the gate length is decreased, a short-channel effect can besuppressed enough thanks to the characteristics of the double-gatetransistors for the field-effect transistors 25 and 26 shown in FIG. 3.With double gate transistors, the gain can be increased even in the caseof suppressing the short channel effect. Because a double-gatetransistor is an intrinsic channel device, the double-gate transistorcan suppress the variation of a threshold voltage, which is caused byrandom dopant fluctuation. A matching characteristics can be improved,even though the field-effect transistors 25 and 26 are differentiallyoperated.

The fins f11 to f19 and f21 to f29 have a small fin width. Although theparasitic resistance of each of the fins f11 to f19 and f21 to f29 islarge, the parasitic resistance between the gate electrode G11 and thegate electrode G13, and the parasitic resistance between the gateelectrode G12 and the gate electrode G14 can be decreased by increasingthe numbers of the fins f11 to f19 and f21 to f29. Therefore, thereduction of the gain can be suppressed. To decrease the parasiticresistance between the gate electrode G11 and the gate electrode G13,the interval between the gate electrode G11 and the gate electrode G13is preferably as small as possible, and the gate electrodes G11 and G13can be superimposed with the wiring H12. To decrease the parasiticresistance between the gate electrode G12 and the gate electrode G14,the interval between the gate electrode G12 and the gate electrode G14is preferably as small as possible, and the gate electrodes G12 and G14can be superimposed with the wiring H13.

By setting the gate length of the gate electrodes G11, G12, and G15larger than the gate length of the gate electrodes G13 and G14,double-gate transistors can be used for the constant current sources 21and 22 shown in FIG. 3. The constant current sources 21 and 22 forsupplying a constant current to the field-effect transistors 25 and 26can be formed in the same fins.

If the fins f11 to f19 and f21 to f29 are aligned at equal intervals,transistors can be formed by a pattern having a simple repetition of astraight line and a space. Therefore, the sizes of the fins f11 to f19and f21 to f29 can be easily managed, and size controllability of thefins f11 to f19 and f21 to f29 can be improved. Consequently, a matchingcharacteristic of a differential analog circuit can be improved.

The numbers of the fins f11 to f19 and f21 to f29 are set to evennumbers to have the symmetrical geometry therefore, the fins f11 to f19and f21 to f29 can be formed by a sidewall transfer process which formsthe fin-fin pair. Further, an arrangement pitch of the fins f11 to f19and f21 to f29 can be reduced by the sidewall transfer process.

Out of the fins f11 to f19 and f21 to f29, the fins f11, f12, f21, andf22 are aligned at both ends, and are used as dummy fins. Therefore,such field-effect transistors can be manufactured, having the patternregularity for the lithography and the etching process. Further, thevariation of a direct current (DC) characteristic of a threshold voltageand the like can be suppressed, and the degradation of short-channeleffect can be also suppressed, because of the excellent patternregularity.

For example, the fins f11 to f19 and f21 to f29 are aligned from thedevice region to device isolation region; i.e. from the region wherefins are regularly placed to the region where the fins are placedwithout the same regularity. In a portion which suddenly changes thepattern regularity to near an isolated pattern, an etching conditionshould be changed, and the bottom portions of the fins f11, f12, f21,and f22 become thick in a tapered shape. Even at a time of applyinglithography, the sizes of fins aligned at both ends are deviated fromthe sizes of fins aligned at the inside.

Therefore, if a field effect transistor is manufactured with enoughpattern regularity, a variability of DC characteristics of thefield-effect transistor can be improved.

If the numbers of the contacts C13 to C16 connected to the wirings H12to H14 are set larger than the numbers of the contacts C11, C12, C17,and C18 connected to the wirings H11 and H15, an effective channel width(=number of fins×height of fins×2) of a current flowing through thefield-effect transistors 25 and 26 in FIG. 3 can be increased, and aneffective channel width of a current flowing through the constantcurrent sources 21 and 22 in FIG. 3 can be decreased at the same time.

Therefore, while decreasing (drain) conductance of the constant currentsources 21 and 22, a current flowing through the field-effecttransistors 25 and 26 can be increased, and the frequency response ofthe field-effect transistors 25 and 26 can be improved.

If the contacts C11 to C15 are symmetrically aligned, a current path canbe shortened because a current, entering the fins f14 and f16 via thecontacts C11, can be spread to whole drain region of the field-effecttransistor 25. Even though the number of the contacts C11 connected tothe wiring H11 is limited, increase of a delay time can be alsosuppressed thanks to the symmetrical contact allocation.

In the first embodiment, a method of using the fins f11, f12, f21, andf22 aligned at both ends as dummy fins, out of the fins f11 to f19 andf21 to f29, is explained. Instead of using each two fins of the finsf11, f12, f21, and f22 aligned at both ends as dummy fins, each one ofthe fins aligned at both ends can be also used as a dummy fin.Alternatively, three or more fins aligned at both ends can be used asdummy fins.

In the first embodiment, a method of forming the contacts C11 and C12 isalso explained which are connected to the wiring H11, in only the finsf14, f16, f24, and f26. However, the number of the contacts C11 and C12connected to the wiring H11 is not necessarily limited to two, and canbe any number larger than that of the contacts C13 and C14 connected tothe wirings H12 and H13, respectively. For example, the contacts C11 andC12 connected to the wiring H11 can be aligned to be formed in only thefins f15 and f25, respectively, or can be aligned to be formed in onlythe fins f13, f15, f17, f23, f25, and f27, respectively.

In the first embodiment, a method of forming the contacts C17 and C18 isalso explained which are connected to the wiring H15, in only the finsf14, f16, f24, and f26, respectively. However, the number of thecontacts C17 and C18 connected to the wiring H15 is not necessarilylimited to two, and can be any number larger than that of the contactsC15 and C16 connected to the wiring H14. For example, the contacts C17and C18 connected to the wiring H15 can be aligned to be formed in onlythe fins f15 and f25, respectively, or can be aligned to be formed inonly the fins f13, f15, f17, f23, f25, and f27, respectively.

A relationship between the gain (=voltage gain) A of the circuit and aresistance value R₁ of the resistors 23 and 24 is explained below by thefollowing equations.

If V_(in1) and V_(in2) represent input voltages of the circuit, and alsoIf V_(out1) and V_(out2) represent output voltages of the circuit, basicequations of the circuit shown in FIG. 3 are given by equations (1) to(7) as follows.

$\begin{matrix}{V_{a} = \frac{I_{1} + I_{2}}{G_{3}}} & (1) \\{{V_{{out}\; 1} - V_{b\; 1}} = {R_{1}I_{1}}} & (2) \\{{V_{{out}\; 2} - V_{b\; 2}} = {R_{1}I_{2}}} & (3) \\{I_{1} = {{g_{m}\left( {V_{{in}\; 1} - V_{a}} \right)} + {\frac{1}{r_{ds}}\left( {V_{b\; 1} - V_{a}} \right)}}} & (4) \\{I_{2} = {{g_{m}\left( {V_{{in}\; 2} - V_{a}} \right)} + {\frac{1}{r_{ds}}\left( {V_{b\; 2} - V_{a}} \right)}}} & (5) \\{V_{dd} = {\frac{I_{1}}{G_{1}} + V_{{out}\; 1}}} & (6) \\{V_{dd} = {\frac{I_{2}}{G_{2}} + V_{{out}\; 2}}} & (7)\end{matrix}$

In the above equations, G₁, G₂, and G₃ represent (drain) conductance ofthe constant current sources 21 and 22, respectively, and I₁, I₂, andI₁+I₂ represent currents flowing through the constant current sources 21and 22, respectively. V_(dd) represents a power source potential, g_(m)represents mutual conductance of the field-effect transistors 25 and 26,V_(a) represents a source potential of the field-effect transistors 25and 26, V_(b1) and V_(b2) represent drain potentials of the field-effecttransistors 25 and 26, respectively, and r_(ds) represents aninclination of an I_(d)−V_(d) characteristic of the field-effecttransistors 25 and 26. I_(d) represents a drain current of thefield-effect transistors 25 and 26, and V_(d) represents a drain voltageof the field-effect transistors 25 and 26.

I₁ and I₂ are obtained from the basic equations of equations (1) to (7),and a relationship between the input voltages V_(in1) and V_(in2) andthe output voltages V_(out1) and V_(out2) is finally obtained.

First, equations (8) and (9) are obtained as follows, by the equations(1), (4), and (5).

$\begin{matrix}{I_{1} = {{g_{m}\left( {V_{{in}\; 1} - \frac{I_{1} + I_{2}}{G_{3}}} \right)} + {\frac{1}{r_{ds}}\left( {V_{b\; 1} - \frac{I_{1} + I_{2}}{G_{3}}} \right)}}} & (8) \\{I_{2} = {{g_{m}\left( {V_{{in}2} - \frac{I_{1} + I_{2}}{G_{3}}} \right)} + {\frac{1}{r_{ds}}\left( {V_{b\; 2} - \frac{I_{1} + I_{2}}{G_{3}}} \right)}}} & (9)\end{matrix}$

Next, equations (10) and (11) are obtained as follows by subtractingV_(b1) and V_(b2) from the equations (8) and (9) by using the equations(2) and (3).

$\begin{matrix}\begin{matrix}{{{\left( {1 + \frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}}} \right)I_{1}} + {\left( {\frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}}} \right)I_{2}}} = {{g_{m}V_{{in}\; 1}} + {\frac{1}{r_{ds}}V_{b\; 1}}}} \\{= {{g_{m}V_{{in}\; 1}} + {\frac{1}{r_{ds}}\left( {V_{{out}\; 1} - {R_{1}I_{1}}} \right)}}}\end{matrix} & (10) \\\begin{matrix}{{{\left( {\frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}}} \right)I_{1}} + {\left( {1 + \frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}}} \right)I_{2}}} = {{g_{m}V_{{in}\; 2}} + {\frac{1}{r_{ds}}V_{b\; 2}}}} \\{= {{g_{m}V_{{in}2}} + {\frac{1}{r_{ds}}\left( {V_{{out}\; 2} - {R_{1}I_{2}}} \right)}}}\end{matrix} & (11)\end{matrix}$

Equations (12) and (13) are obtained as follows by arranging theequations (10) and (11) by I₁ and I₂.

$\begin{matrix}{{{\left( {1 + \frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}} + \frac{R_{1}}{r_{ds}}} \right)I_{1}} + {\left( {\frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}}} \right)I_{2}}} = {{g_{m}V_{{in}\; 1}} + {\frac{1}{r_{ds}}V_{{out}\; 1}}}} & (12) \\{{{\left( {\frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}}} \right)I_{1}} + {\left( {1 + \frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}} + \frac{R_{1}}{r_{ds}}} \right)I_{2}}} = {{g_{m}V_{{in}\; 2}} + {\frac{1}{r_{ds}}V_{{out}\; 2}}}} & (13)\end{matrix}$

An equation (14) is obtained as follows by writing the the equations(12) and (13) by using a matrix and a vector format.

$\begin{matrix}{{\begin{pmatrix}{1 + \alpha + \frac{R_{1}}{r_{ds}}} & \alpha \\\alpha & {1 + \alpha + \frac{R_{1}}{r_{ds}}}\end{pmatrix}\begin{pmatrix}I_{1} \\I_{2}\end{pmatrix}} = {{g_{m}\begin{pmatrix}V_{{in}\; 1} \\V_{{in}\; 2}\end{pmatrix}} + {\frac{1}{r_{ds}}\begin{pmatrix}V_{{out}\; 1} \\V_{{out}\; 2}\end{pmatrix}}}} & (14)\end{matrix}$

An equation (15) is obtained as follows by solving I₁ and I₂ by theequation (14).

$\begin{matrix}{\begin{pmatrix}I_{1} \\I_{2}\end{pmatrix} = {\frac{1}{\left( {1 + \alpha + \frac{R_{1}}{r_{ds}}} \right)^{2} - \alpha^{2}}{\begin{pmatrix}{1 + \alpha + \frac{R_{1}}{r_{ds}}} & {- \alpha} \\{- \alpha} & {1 + \alpha + \frac{R_{1}}{r_{ds}}}\end{pmatrix}\left\lbrack {{g_{m}\begin{pmatrix}V_{{in}\; 1} \\V_{{in}\; 2}\end{pmatrix}} + {\frac{1}{r_{ds}}\begin{pmatrix}V_{{out}\; 1} \\V_{{out}\; 2}\end{pmatrix}}} \right\rbrack}}} & (15)\end{matrix}$

In the above equations, α is defined by an equation (16) shown below.

$\begin{matrix}{\alpha \equiv \left( {\frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}}} \right)} & (16)\end{matrix}$

I₁ and I₂ are solved by the equations (6) and (7), and are changed intoa matrix and a vector format, thereby obtaining an equation (17) asfollows.

$\begin{matrix}{\begin{pmatrix}I_{1} \\I_{2}\end{pmatrix} = {{G_{1}\begin{pmatrix}{V_{dd} - V_{{out}\; 1}} \\{V_{dd} - V_{{out}\; 2}}\end{pmatrix}} = {{G_{1}\begin{pmatrix}V_{dd} \\V_{dd}\end{pmatrix}} - {G_{1}\begin{pmatrix}V_{{out}\; 1} \\V_{{out}\; 2}\end{pmatrix}}}}} & (17)\end{matrix}$

I₁ and I₂ are erased from the equations (15) and (17), thereby obtainingan equation (18) as follows.

$\begin{matrix}{{{G_{1}{M\begin{pmatrix}V_{dd} \\V_{dd}\end{pmatrix}}} - {g_{m}{r_{ds}\begin{pmatrix}V_{{in}\; 1} \\V_{{in}\; 2}\end{pmatrix}}}} = {\left( {E + {G_{1}M}} \right)\begin{pmatrix}V_{{out}\; 1} \\V_{{out}\; 2}\end{pmatrix}}} & (18)\end{matrix}$

In the above equation, β is defined by an equation (19) shown below.

β≡αr_(ds)   (19)

M is defined by an equation (20) shown below.

$\begin{matrix}{M \equiv \begin{pmatrix}{r_{ds} + \beta + R_{1}} & \beta \\\beta & {r_{ds} + \beta + R_{1}}\end{pmatrix}} & (20)\end{matrix}$

V_(out1) and V_(out2) are solved by the equation (18), thereby obtainingequations (21) and (22) as follows.

$\begin{matrix}{V_{{out}\; 1} = {{\left( {1 - \frac{1}{a + b}} \right)V_{dd}} + {\frac{{- g_{m}}r_{ds}}{a^{2} - b^{2}}\left( {{aV}_{{in}\; 1} - {bV}_{{in}\; 2}} \right)}}} & (21) \\{V_{{out}\; 2} = {{\left( {1 - \frac{1}{a + b}} \right)V_{dd}} + {\frac{{- g_{m}}r_{ds}}{a^{2} - b^{2}}\left( {{- {bV}_{{in}\; 1}} + {aV}_{{in}\; 2}} \right)}}} & (22)\end{matrix}$

In the above equations, a and b are defined by an equation (23) shownbelow.

$\begin{matrix}{\begin{pmatrix}{1 + {G_{1}{r_{ds}\left( {1 + \frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}}} \right)}} + {G_{1}R_{1}}} & {G_{1}{r_{ds}\left( {\frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}}} \right)}} \\{G_{1}{r_{ds}\left( {\frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}}} \right)}} & {1 + {G_{1}{r_{ds}\left( {1 + \frac{g_{m}}{G_{3}} + \frac{1}{r_{ds}G_{3}}} \right)}} + {G_{1}R_{1}}}\end{pmatrix} = \begin{pmatrix}a & b \\b & a\end{pmatrix}} & (23)\end{matrix}$

A differential voltage V_(out2)−V_(out1) is obtained by the equations(21) and (22), thereby obtaining an equation (24) as follows.

$\begin{matrix}\begin{matrix}{{V_{{out}\; 2} - V_{{out}\; 1}} = {\left( {{- g_{m}}r_{ds}} \right)\frac{1}{a^{2} - b^{2}}\left( {{- {bV}_{{in}\; 1}} + {aV}_{{in}\; 2} - {aV}_{{in}\; 1} + {bV}_{{in}\; 2}} \right)}} \\{= {\frac{\left( {{- g_{m}}r_{ds}} \right)}{a - b}\left( {V_{{in}\; 2} - V_{{in}\; 1}} \right)}} \\{= {\frac{\left( {{- g_{m}}r_{ds}} \right)}{1 + {G_{1}r_{ds}} + {G_{1}R_{1}}}\left( {V_{{in}\; 2} - V_{{in}\; 1}} \right)}}\end{matrix} & (24)\end{matrix}$

The gain A of this circuit is defined asA=|(V_(out2)−V_(out1))/(V_(in2)−V_(in1))|, therefore, the gain A can beexpressed by the equation (24) to an equation (25).

$\begin{matrix}\begin{matrix}{A = {\frac{V_{{out}\; 2} - V_{{out}\; 1}}{V_{{in}\; 2} - V_{{in}\; 1}}}} \\{= \frac{g_{m}r_{ds}}{1 + {G_{1}r_{ds}} + {G_{1}R_{1}}}} \\{= \frac{1}{\left( \frac{1}{g_{m}r_{ds}} \right) + \frac{G_{1}}{g_{m}} + \frac{G_{1}R_{1}}{g_{m}r_{ds}}}}\end{matrix} & (25)\end{matrix}$

It is clear from the equation (25) that if the (drain) conductance ofthe constant current sources 21 and 22 and the resistors 23 and 24cannot be disregarded, to increase the gain A, either g_(m)×r_(ds) isincreased, or G₁ is decreased, or R₁ is decreased.

If a condition of G₁×R₁<g_(m)×r_(ds) for the third term of thedenominator is satisfied, the gain A can be increased even though theresistors 23 and 24 cannot be disregarded.

FIG. 4 is a plan view of a layout configuration of a semiconductordevice according to a second embodiment of the present invention.

In FIG. 4, plural fins f31 to f38 and f41 to f48 are aligned in parallelwith each other. Preferably, the width of each of the fins f31 to f38and f41 to f48 is equal to each other, and the interval between fins ofthe fins f31 to f38 and f41 to f48 is equal to each other. Preferably,the total number of the fins f31 to f38 and the total number of the finsf41 to f48 are even numbers. A semiconductor material can be used forthe material of the fins f31 to f38 and f41 to f48. For example, thematerial can be selected from Si, Ge, SiGe, SiC, SiSn, PbS, GaAs, InP,GaP, GaN, ZnSe, and GaInAsP.

For the fins f33 to f38 and f43 to f48, gate electrode G21 is formed onboth side surfaces of the fins f33 to f38 and f43 to f48 to cross thefins f33 to f38 and f43 to f48.

For the gate electrodes G21, gate electrodes G22 and G23 are aligned inparallel at a predetermined interval. For the fins f33 to f37, the gateelectrode G22 is formed on both side surfaces of the fins f33 to f37 tocross the fins f33 to f37. For the fins f43 to f47, the gate electrodeG23 is formed on both side surfaces of the fins f43 to f47 to cross thefins f43 to f47.

For the gate electrodes G22 and G23, gate electrode G24 is aligned inparallel at a predetermined interval. For the fins f33 to f37 and f43 tof47, the gate electrode G24 is formed on both side surfaces of the finsf33 to f37 and f43 to f47 to cross the fins f33 to f37 and f43 to f47.

Preferably, the gate electrode G21 can have a larger gate length thanthat of the gate electrodes G22 to G24. Preferably, a drain resistancein a saturation region of transistors having the gate electrode G21 isset to be assumed that it is substantially infinite(dI_(d)/dV_(d)=1/R_(d) to 0). Preferably, the gate length of the gateelectrodes G22 to G24 is set as small as possible to increase mutualconductance and to increase gain, and can be set equal to or smallerthan 30 nanometers, for example.

Source/drain layers are formed in the fins f34 to f37 and f44 to f47 atboth sides of the gate electrodes G21 to G24, respectively. Thesource/drain layers formed in the fins f34 to f37 between the gateelectrode G21 and the gate electrode G22 are shared by the gateelectrodes G21 and G22. The source/drain layers formed in the fins f44to f47 between the gate electrodes G21 and G23 are shared by the gateelectrodes G21 and G23. The source/drain layers formed in the fins f34to f37 between the gate electrodes G22 and G24 are shared by the gateelectrodes G22 and G24. The source/drain layers formed in the fins f44to f47 between the gate electrodes G23 and G24 are shared by the gateelectrodes G23 and G24.

The fins f34 to f37 and f44 to f47 at a drain side at the side of thegate electrode G21 is connected to a wiring H21 via contacts C21 andC22, respectively. The fins f34 to f37 at a source side at the side ofthe gate electrode G21 is connected to a wiring H23 via contacts C23.The fins f44 to f47 at a source side at the side of the gate electrodeG21 is connected to a wiring H24 via contacts C24. The fins f34 to f37and f44 to f47 at a source side at the side of the gate electrode G24 isconnected to a wiring H27 via contacts C25 and C26, respectively.

The gate electrode G21 is connected to a wiring H22 via contacts C27 andC28, respectively. The gate electrode G22 is connected to a wiring H25via contacts C29, and the gate electrode G23 is connected to the wiringH25 via contacts C30. The gate electrode G24 is connected to a wiringH26 via contacts C31. Metals such as Al, AlSiCu or Cu can be used forthe material of the wirings H21 to H27.

Preferably, the contacts C22 to C26 are symmetrically aligned,respectively. Preferably, the gate electrodes G22 and G23 are alignedsymmetrically with each other, and preferably, the wirings H23 and H24are aligned symmetrically with each other. Embedded wirings formed onthe fins f34 to f37 and f44 to f47 can be used for the contacts C21 toC26.

Out of the fins f31 to f38 and f41 to f48, the fins f31 to f32 and f41and f42, those are aligned at both ends, can be used as dummy fins; Theycan not be used as a part of field-effect transistors.

FIG. 5 depicts an equivalent circuit of the semiconductor device shownin FIG. 4. The equivalent circuit is used for a mixer circuit or thelike.

In FIG. 5, resistors 33 and 34 are connected to drains of field-effecttransistors 35 and 36, respectively. A drain of a field-effecttransistor 37 is connected in common to sources of the field-effecttransistor 35 and 36. The resistors 33 and 34 can be configured byconstant current sources.

The resistor 33 can be configured by the gate electrode G21 and the finsf34 to f37 shown in FIG. 4. The resistor 34 can be configured by thegate electrode G21 and the fins f44 to f47 shown in FIG. 4. Thefield-effect transistor 35 can be configured by the gate electrode G22and the fins f34 to f37 shown in FIG. 4. The field-effect transistor 36can be configured by the gate electrode G23 and the fins f44 to f47shown in FIG. 4. The field-effect transistor 37 can be configured by thegate electrode G24 and the fins f34 to f37 and f44 to f47 shown in FIG.4.

The wiring H21 shown in FIG. 4 is connected to the power sourcepotential V_(dd), and the wiring H27 is connected to the groundpotential V_(ss). If the input voltages V_(in1) and V_(in2) are input tothe gate electrodes G22 and G23, respectively, and also if an inputvoltage IN2 is input to the gate electrode G24, the output voltagesV_(out1) and V_(out2) are output from the wirings H23 and H24,respectively. As a result, a product of an input voltageIN1=V_(in1)−V_(in2) and an input voltage IN2 is output as an outputvoltage OUT=V_(out1)−V_(out2), thereby causing the field-effecttransistors operate as mixers (multipliers).

Even though a gate length is decreased, a short-channel effect can besuppressed by using double-gate transistors for the field-effecttransistors 35 to 37 shown in FIG. 5. Gain can be increased whilesuppressing degradation of a cutoff characteristic. A matchingcharacteristic if the field-effect transistors 35 and 36 aredifferentially operated can be improved.

If the gate electrodes G22 and G23 are aligned to cross the plural finsf34 to f37 and f44 to f47, respectively, the parasitic resistancebetween the gate electrodes G21 and G22 and the parasitic resistancebetween the gate electrodes G21 and G23 can be decreased. Therefore,reduction of gain can be suppressed.

To decrease the parasitic resistance between the gate electrodes G21 andG22, the interval between the gate electrodes G21 and G22 is preferablyas small as possible. It is also required that the gate electrodes G21and G22 can be superimposed with the wiring H23. To decrease theparasitic resistance between the gate electrodes G21 and G23, theinterval between the gate electrodes G21 and G23 is preferably as smallas possible. It is also required that the gate electrodes G21 and G23can be superimposed with the wiring H23.

If the gate length of the gate electrodes G21 is set larger than that ofthe gate electrodes G22 to G24, double-gate transistors can work as theresistors 33 and 34, as shown in FIG. 4. The resistors 33 and 34connected to the field-effect transistors 35 and 36 can be formed in thesame fins.

If the fins f31 to f38 and f41 to f48 are aligned at equal intervals,fin size controllability for the fins f31 to f38 and f41 to f48 can beimproved. Consequently, a matching characteristic of a differentialanalog circuit can be improved.

The numbers of the fins f31 to f38 and f41 to f48 are set to evennumbers, therefore, symmetry can be improved. The fins f31 to f38 andf41 to f48 can be formed by a sidewall transfer process. Further, anarrangement of the fins f31 to f38 and f41 to f48 can be reduced.

Out of the fins f31 to f38 and f41 to f48, the fins f11, f12, f21, andf22 are aligned at both ends, and are used as dummy fins. Therefore,such field-effect transistors can be manufactured, having the patternregularity for the lithography and the etching process. Further, thevariation of a DC characteristic of a threshold voltage and the like canbe suppressed, and the degradation of short-channel effect can be alsosuppressed, because of the excellent pattern regularity.

If the numbers of the contacts C23 to C26 connected to the wirings H23,H24, and H27 are set larger than the numbers of the contacts C21 and C22connected to the wiring H21, conductance of the resistors 33 and 34 canbe decreased, and a current flowing to the field-effect transistors 35and 36 can be increased, thereby improving the speed of the field-effecttransistors 35 and 36.

If the contacts C21 to C26 are symmetrically aligned, a current path canbe shortened because a current, entering the fins f34 and f36 via thecontacts C21, can be spread to whole drain region of the field-effecttransistor 35.

Even though the number of the contacts C11 connected to the wiring H11is limited, increase of a delay time can be also suppressed thanks tothe symmetrical contact allocation.

In the second embodiment, a method of using the fins f31, f32, f41, andf42, aligned at both ends as dummy fins out of the fins f31 to f38 andf41 to f48, is explained. Instead of using each two fins of the finsf31, f32, f41, and f42 aligned at both ends as dummy fins, each one ofthe fins aligned at both ends can be also used as a dummy fin.Alternatively, three or more fins aligned at both ends can be used asdummy fins.

In the second embodiment, a method of forming the contacts C21 and C22connected to the wiring H21 is explained, in only the fins f34, f36,f44, and f46. However, the number of the contacts C21 and C22 connectedto the wiring H21 is not necessarily limited to two, and can be anynumber larger than that of the contacts C23 and C24 connected to thewirings H23 and H24, respectively.

FIGS. 6A, 7A, 8A, and FIG. 9A are plan views of a method ofmanufacturing a fin structure according to a third embodiment of thepresent invention, and FIGS. 6B, 7B, 8B, and FIG. 9B are cross-sectionalviews of FIGS. 6A, 7A, 8A, and FIG. 9A, cut along a line A1-A1′, lineA2-A2′, line A3-A3′, and line A4-A4′, respectively.

In FIGS. 6A and 6B, a semiconductor layer 53 is formed on asemiconductor substrate 51 via an insulation layer 52. For thesemiconductor substrate 51 on which the semiconductor layer 53 is formedvia the insulation layer 52, an SOI substrate can be used, for example.

Dummy patterns R1 made of a first material are formed on thesemiconductor layer 53. For the dummy patterns R1, linear patternsaligned in parallel with each other at a predetermined interval can beused. The interval between the dummy patterns R1 can be set as 2×F+H,where F represents the width of each fin 54 formed on the insulationlayer 52, and H represents the interval between the finally formed fins54.

As shown in FIGS. 7A and 7B, an insulation film made of a secondmaterial is formed on the semiconductor layer 53 so that a gap betweenthe dummy patterns R1 is filled. By etching the insulation film by usinganisotropic etching such as reactive ion etching (RIE), sidewallpatterns R2 and R3 are formed on sidewalls of the dummy patterns R1.Film thicknesses of the sidewall patterns R2 and R3 can be controlled byan initial film thickness of the insulation film formed on thesemiconductor layer 53 and by an etching time.

The dummy patterns R1 are etched by using a difference of etching rate(=by utilizing etching selectivity) between the first material and thesecond material. Then, the dummy patterns R1 are removed from thesemiconductor layer 53 by leaving the sidewall patterns R2 and R3 on thesemiconductor layer 53, as shown in FIGS. 8A and 8B.

Anisotropic etching such as RIE is performed to the semiconductor layer53 by using the sidewall patters R2 and R3 as etching masks, therebyforming the fins 54 on the insulation layer 52, as shown in FIGS. 9A and9B.

By the above arrangement, the fins 54 can be formed at a pitch two timesof the resolution limit of a lithography process. As a result, thedensity of the fins 54 can be increased.

If the fins 54 are formed on the insulation layer 52, gate electrodesare formed on both side surfaces of the fins 54 to cross the fins 54 viagate dielectric films, and source/drain layers of the fins 54 areconnected to a wiring via contacts, thereby manufacturing double-gatetransistors shown in FIG. 1 or FIG. 4.

Additional advantages and modifications will readily occur to thoseskilled in the art. Therefore, the invention in its broader aspects isnot limited to the specific details and representative embodiments shownand described herein. Accordingly, various modifications may be madewithout departing from the spirit or scope of the general inventiveconcept as defined by the appended claims and their equivalents.

1. A semiconductor device comprising: N (N is an integer equal to orlarger than 2) fins made of a semiconductor material aligned in parallelwith each other; a first gate electrode formed on both side surfaces ofeach of the N fins to cross the fins; and a second gate electrode formedin parallel with the first gate electrode on both side surfaces of the Nfins to cross the fins, and having a larger gate length than a gatelength of the first gate electrode, wherein number of fins formed withcontacts of source/drain layers of first field-effect transistors havingthe first gate electrode is larger than number of fins formed withcontacts of source/drain layers of second field-effect transistorshaving the second gate electrode.
 2. The semiconductor device accordingto claim 1, further comprising at least one dummy fin aligned inparallel at outside of the N fins.
 3. The semiconductor device accordingto claim 1, wherein widths of the fins are equal to each other, andintervals between the fins are also equal to each other.
 4. Thesemiconductor device according to claim 1, wherein the contacts of thesource/drain layers of the first field-effect transistors are aligned ineach of the fins to be symmetrical with each other in the top viewplain, and the contacts of the source/drain layers of the secondfield-effect transistors are aligned in each of the fins to besymmetrical with each other in the top view plain.
 5. The semiconductordevice according to claim 1, wherein the fins are not doped withimpurity.
 6. The semiconductor device according to claim 1, wherein apart of the gate electrode is configured by metal compounds.
 7. Thesemiconductor device according to claim 1, wherein if G represents drainconductance of the second field-effect transistors, g_(m) representsmutual conductance of the first field-effect transistors, r_(ds)represents a drain resistance, and R represents a parasitic resistanceat a drain side, a relationship of G×R<g_(m)×r_(ds) is satisfied.